Mathematical modelling of reaction kinetics applied for industrial dihydrate method of P 2 O 5 production

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1 Euron ymosum on Comur Ardd Add Pross Engnrng L. Pugjnr nd A. Esuñ (Eors) Elsvr n B.. All rghs rsrvd. hml modllng o ron kns ld or ndusrl dhydr mhod o P O roduon I.. obolv, E.. Kolsov Drmn o Cybrns o Chml Engnrng, ndlyv Chml- Thnologl nvrsy o Russ (CTR) ussky sq. 9, osow, Russ, 7 Absr Tl. 7(9) , Fx (9), E-ml: sobolv@rml.ru Kns o lum sul rysllzon durng h ross o hoshor d xron ws sudd n hs work. hnsms o lum sul rysl nulon nd growh wr ound ou. Connuous orgnl mhod o yl sulur d d ws dvlod or h ndusrl hoshor d roduon by dhydr mhod rsuld n sgnn nrsng o roduon yld. Kywords: modllng, hoshor d, dhydr mhod. Inroduon Ad mhods o hoshorus-onnng ors rmn r h mn or hoshor rlzrs obnng. or hn 6 % o hoshorus onnng rlzrs ll ovr h world s rodud on h bss o xron hoshor d, h mn mhods o s roduon bng dhydr mhod. Th ross o hoshor d xron s onurrn ross nludng boh nurl hoshs dssoluon n sulur d soluons nd rysllzon o lum sul modons (lum sul dhydr or lum sul hmhydr) dndng on dhydr, hmhydr or dhydr - hmhydr mhods rrd ou undr drn mrurs onons. n uros o hs r ws o nvsg xrmnlly nd by mns o mhml modllng kns o mn rosss ourrng durng dhydr mhod o hoshor d xron, nmly: kns o hoshs dssoluon, o ssvon lm ormon on hoshs grns, o lum sulh dhydr nulon nd growh n soluon; o nd ou oml onons or ndusrl dhydr ross nd, on h bss o xrmnl nd omur nvsgons o kns, o roos nw mhod o xron hoshor d roduon by dhydr mhod, onssng n orgnson o yl sulhur d d.. Objvs nd hnqus o mhml modllng o ron kns ld or dhydr mhod o hoshor d xron

2 Lborory nd ndusrl xrmnl umuld mrls llowd us o rry ou nlyss o hoshs dssoluon nd lum sulh rysllson lmnry s nd o dn y o rosss r dndns on hr movng ors. For h lum sulh rysllson dsron h mhnsm o homognous nulon nd rysls' growh n h kn r s d. hm o h rosss nron, dsrbd by h mhml modl, s shown n h g.. ssvon C (D,) (,) (I) ( C j) C O C duson ( ) dsso- surs- nul- rysl growh luon uron on Fgur. hm o hysl-hml hnomn nron n h ombnd mhml modl o hoshs dssoluon nd lum sulh rysllson rosss. ovng ors y o hoshs dssoluon nd rysllson rosss r bsd on h quon o unvrsl mss rnsr movng or, nludng nhly omonn, vloy omonn o non-qulbrum hss nd on drns n hml onls o dssolvd subsn n h low or nd nr h hss' nr sur. Formng longsd wh hoshor d lum sul dhydr hs sh o srhd rllld. Thror whn modlng lum sul dhydr roduon w should onsdr growh o wo s. Tkng no oun h boh rosss (hoshor dssoluon nd lum sulh rysllzon) r dsrbd whn h rmwork o dl mxng sohrml ror modls h ollowng quons or vlos o h mn rosss wr dvlod: or hoshor rls dssoluon r nd ssvon lmng r : K D l 6 Kh q R bl C C ; ; () or lum sulh nulon r I, or vrg r o lum sulh rysl growh j on lnr rmrs L j : I K n C C ; C j K C C j C, () m j

3 whr nd - h dnss o nd ssvon lms wh h hknss h; D - molulr duson or, =dl/ - lnr r o hosh rl szs rnsormons h dssoluon; - s y on mxng; l - sz o hosh rls ; h - hknss o sulur lm on hosh surs; n - vsosy; - r o dssolvng, C nd C - ul nd qulbrum onnrons o O n hoshor d soluons, ordngly. K, R,, b, q - onsns. For h dsron o sulh lum mss rysllson nd olydsrsd hoshor dssoluon h quons or h rls' sz dsrbuon unons wr usd. Th rls nsmbl voluon o hoshor ws xmnd n wodmnsonl hs s wh o-ordns: l - sz o hoshor non-dssolvd grn, h - hknss o h ssvon lm. For h rysllson ross wo hrrs lnr szs o rysl L nd L wr sld s hs s o-ordns. For dsron o dssoluon ross xrmnl d, rvd by h mhod o rdov soos on lborory nsllon wr usd. Th mhml modl o xron hoshor d roduon undr h rod onons or dhydr ross ws dvlod on h bss o mnond bov quons. As rsul o mhml modllng h dssoluon r o olydsrsd omoson hoshor, h r o nulon nd h rysl growh r wr luld, kn onsns wr ound For modlng mss rysllzon o lum sul dhydr, zro momn nd rs wo momns nd o dsrbuon unon dnsy on sz or lum sul rysls. orovr, vrg sz o j-h glly o rysl s: <l l > j = j /, j=, For ndusrl onnuous ross o hoshor d xron h rngulr nsonl ror wh h workng y o 7 m ws hosn s h mos wdly srd y o rors usd n hoshor d roduon. Tkng no onsdron numbr o ssumons, hs y o ror n b dsrbd s h modl onssng o v uns o dl mxng wh h ollowng ross low dgrm: Fg. Pross low dgrm or onnuous ndusrl ross ngron, whr - volum low rs o h sulhur nd hoshor ds;,, - volum low rs o, ul on sg o lron nd rulon;

4 - - s o uns, orrsondng o h y o wo djn sons o smuld ror; - ul low no un o ror modl h s qul o h moun o lodd rgns. Aordng o h low shm mnond bov h quons or blns o rls nd dhydr lum sulh rysls or un o ror modl r : h l 6 () I d () For h omonn o lqud hs h smlr mrl bln quons wr dvlod. o h quon or sulhur d onnron hs o h orm o: C,, C d P d () Equon or hoshor d onnron: d J d (6) Equon or lum sulh onnron n lqud hs:

5 d C C d J C C J C P,, C C C C (7) C whr - molulr wgh o omonn, I = o o L (r+b)/lh, I = o o L b/lhrs o nulon, L, l - mxmum nd mnmum szs o hosh rls, - mxmum sz o hknss o sulur lm; r- volum o hosh rls; b - volum o sulur lm. Equons ysm ()-(7) rsns sl mhml modl bs, dsrbng mn hysl hml rosss, whh k l n ndusrl rus. For rmnon o rysllson ross kn rmrs h srs o xrmns on ndusrl nsllon ws rrd ou. Whn rossng h xrmns rsuls h ollowng unon y ws usd s unblnd rron: n k C k C k k k k F k k C k k k k k L L k Lk k L L k Lk k (8). Rsuls nd onlusons. As rsul o mhml modllng h dssoluon r o olydsrsd omoson, h r o nulon nd h rysl growh r or h un o ror wr luld. I ws shown h n h ndusrl ror ll h rosss rlly r ovr n h h-sxh sons (n h hrd un o h modl) nd roxmly 6% o ror workng y rovds h horl y. Th's why ws s h roblm o dvlong suh xron hoshor d roduon mhod whh wll rovd h ull ouon o ror workng y n ordr o nrs h roduvy nd o rs P O xron or. I wll rsul n svng o rw mrls nd owr onsrvon. W dvlod h hoshor d roduon mhod n h non-sdy-s hnologl onons. As onrol rmr whn rlsng hs onons h sulhur d low r n h ror ws hosn. In h g. h urvs o sulhur d onnron onsrnd osllon nd xron dgrs or h non-sdys sulh onons r shown. As n b sn rom h gur h onrnd mhod o ross orgnson llows us o r wo sulh lvls, orrsondng o h omum onons o dssoluon nd rysllson rosss durng h sy m

6 n h ror zon. By mns o mhml modl h oml vlus o mlud nd rquns o sulhur d low r rod osllon wr obnd. Th ndusrl ss o dvlod hnologl onons wr rrd ou nd hy hv onrmd ny o h dvlod xron hoshor d roduon mhod. Fgur. Alrons o h ross hrrss undr h non-sdys onons. - n -s un (lulon), - n -nd un (lulon), - n -d un o ror (xrmn), - h xron on n -nd un o h modl. Ls o lrur.. obolv I.. hml modllng nd omzon o hoshor d xron rosss by dhydr-hmhydr mhod rom hoshors Kru./Ph.D. hss. -osow, E.. Kolsov, I.A. Provlovskj, I.. obolv, A.. Gns,.A. slnko, Ws ulzon nd owr onsrvon n ndusrl roduon on h bss o mhml modllng mhods // nd Conrn on Pross Ingron, odllng nd Omson or Enrgy vng nd Polluon Rduon, PRE' 99, 999, Buds, ungry, I.. obolv, A.. Jns,.B. Glbov, I.A. Provlovsky, E.. Kolsov, L.. Gordv, hml smulon o ngrd ross o sold-hs xron nd rysllzon ( h xml o hoshor d obnng) // rd Euron Congrss o Chml Engnrng, ECCE,, Nurmbrg, Grmny,. 6 (bsr), (ull x s on CD-RO ).